Some corrections, if I may:
While personally i have no read many books about it, apart from some about the last years, after the battle of Matzikert, and i had a vague impression from school, i like the symbolic element of the empire, being a lighthouse of civilization surrounded by barbarism, although i do not, naturally, like the fact that ultimatelly it fell to such barbarism.
Manzikert, I presume, 1071. An ominous battle...
I adore its emblems, which is why one of them is my Avatar. The double headed eagle, which meant that the empire consisted of lands in both sides of the bosporus, in two continents (at an earlier time in three continents) can also be seen as symbolic, and could signify on a personal level the double existence of man, being both a creature of the senses and of imagination, and of course the eagle being a symbol of power.
According to Diarmaid MacCulloch the double eagle, adopted in 1000 AD stands for East and West (Roman Empire that is). I also doubt if the concept of ruling in two continents was very important at the time (if indeed the concept had already been developed), nor ruling both sides of the Bosporus (which isn't
that big).
But the ancient Russians called them Greeks!
I'm sure you mean medieval Russians?
Russia took that symbol for herself. It now symbolizes Russia's connections to Europe and Asia (or the double rule of Putin and Medvedev, as you wish).
Indeed: the 'Russian' double eagle was a czarist adoption of the extinct Byzantines' emblem; hence the concept of Russia as the third Rome.
As Byzantium was indirectly responsible for the christianization of Eastern Europe - in large part due to two monks, one of whom invented the Cyrillic alphabet -, it was in essence father to the present day Orthodox churches of Eastern Europe (not to mention the influence of that Byzantine invention, the icon).
Oh please. The Byzantines didn't kept Muslims expansion from Latin Europe. They hated the West. They hold had been more than happy to let the Muslims bypass the empire if they promised only to destroy Catholic Europe. Heck the entire Crusade was basically this, just switch Muslim with Catholic, a diplomatic ploy by Constantinople to take one enemy to kill off another enemy while gaining land at little lost.
In essence historically incorrect: the Byzantine distrust of Catholic Christians only turned to hatred with the Fourth Crusade, which, instead of marching to the Holy Land, turned on their fellow Christians. Also, the history of the Eastern Empire (strictly speaking the Roman Empire) shos repated efforts to regain what was lost after the fall of Rome until the onslaught of Islam reversed fortune irrevocably, taking two thirds of the then empire.
Rather than casting this argument in terms of military power, battles, and the like, I'd like to see some information about what it was actually like to live in the Byzantine empire. Were its citizens better off - materially or otherwise - than their contemporaries in other societies? That's the only criterion of "greatness" that really counts, but no-one has addressed it at all.
That's rather a modern way to look at The Byzantine Empire. I'm not sure of social historians have addressed this particular issue. There may very well be a Social History of Byzantium (there are several of Rome); perhaps Dachs or Ajidica knows of one?
That apart, doesn't the greatness of Byzantium - as already mentioned - also lie in the ancient heritage combined with the Orthodox Church?